Racket

Question 1

Write a basic lambda the returns the second element in a list (assume there are more than 2 elms in list)?

Answer 1

((lambda (x) ;; declare params
(cadr x)) ;; expression
(list 1 2 3));; actual values

Question 2

Define a function that takes list and a value then checks if all the values in the list are greater than the value?

Answer 2

(define (larger ls n)
(andmap
(lambda (x) (> x n))
ls))

Question 3

Define a function that takes 2 ints as lower and upper bound (inclusive) and should return the largest square that is even?

Answer 3

(define (largestSquare x y)
  (apply max 
         (filter even? (drop 
                        (build-list (+ y 1) (lambda (x) (* x x)))
                        x))))

(largestSquare 1 10)

Question 4

What is currying?

Answer 4

TBD

Question 5

What is the general for of Let?

Answer 5

;; general form of let
(let ((name1 value1)
      (name2 value2)
      ...
      (nameN valueN))
   expression1
   expression2
   ...
   expressionQ)

Question 6

What is the If form?

Answer 6

(if condition true_expression false_expression)

(if (= 0 1) (/ 1 0) (+ 2 3)) => 5
; note that the (/ 1 0) is not evaluated

Question 7

Define a function that calculates the sum of a list?

Answer 7

(define (sum xs)
(if (null? xs)
0
(+ (car xs) (sum (cdr xs)))))

Question 8

What is a thunk?

Answer 8

Delay evaluation by putting an expression in a function!

– Thanks to closures, can use all the same variables later

Question 9

Define a function that squares and returns odd numbers in a list?

Answer 9

(define (square-odd x)
(map (lambda (y) (* y y))
(filter odd? x)))

(square-odd (list 1 2 3 4 5))

Question 10

Define a function that adds 1 to each element in a list.

Answer 10

(define (add1 x)
  (if (null? x)
      '()
      (cons (+ 1 (car x))
            (add1 (cdr x)))))

(add1 (list 1 2 3 4))

Question 11

What is foldl?

Answer 11

Like map, foldl applies a procedure to the elements of one or more lists. Whereas map combines the return values into a list, foldl combines the return values in an arbitrary way that is determined by proc.

(foldl proc init lst)

> (foldl cons ‘() ‘(1 2 3 4))
‘(4 3 2 1)
(foldl + 0 ‘(1 2 3 4))
10

Question 12

What does ZIP do?

Answer 12

Zipping combines two lists into a single list of pairs element-wise.

Question 13

Define a myzip?

Answer 13

(define (myzip ls1 ls2)
  (cond 
    [(null? ls1) ls2]
    [(null? ls2) ls1]
    [else
      (cons (list (car ls1) (car ls2))
            (myzip (cdr ls1) (cdr ls2)))]))

(myzip ‘() ‘(a b c))
(myzip ‘(1 2 3) ‘())
(myzip ‘(1 2 3) ‘(a b c))

Question 14

Define a myfoldl?

Answer 14

(define (myfoldl func init lst)
  (cond
    [(empty? lst) init]
    [else 
     (myfoldl func (func (car lst) init) (cdr lst))]))

(myfoldl cons ‘() ‘(a b c))
(myfoldl + 0 ‘(1 2 3))

Question 15

What is the difference between eq? eqv? and equal?

Answer 15

eq? is pointer comparison.

eqv? is like eq? but does the right thing when
comparing numbers. For number use = to compare as it coercses into crest type

equal? returns true if its arguments have the same
structure.

Question 16

Define a mymap?

Answer 16

(define (my-map f s)
(if (null? s)
‘()
(cons (f (car s)) (my-map f (cdr s)))))

Question 17

Define a myfilter?

Answer 17

(define (my-filter f s)
(cond ((null? s) ‘())
((f (car s)) (cons (car s) (my-filter f (cdr s))))
(else (my-filter f (cdr s)))))

Question 18

Define a sum?

Answer 18

(define (sum s)
(apply + s))

(sum ‘(1 2 3)) => 6

Question 19

What does apply do? And how to use for conditionals and there functions?

Answer 19

The apply function applies a function to a list of its
arguments.

Examples:
(apply even? ‘(3)) => #f
(apply + ‘(1 2 3 4)) => 10

Question 20

What is map and provide examples.

Answer 20

Applies proc to the elements of the lsts from the first elements to the last.

(map function list) ;; general form
(map null? ‘(3 () () 5)) => ‘(#f #t #t #f)
(map round ‘(3.3 4.6 5.9)) => ‘(3.0 5.0 6.0)
(map cdr ‘((1 2) (3 4) (5 6))) => ‘((2) (4) (6))
(map (lambda (x) (* 2 x)) ‘(3 4 5)) => ‘(6 8 10)

Question 21

What is filter and provide an example?

Answer 21

It applies a filter to the list.

filter (lambda (n) (> n 10)) ‘(5 10 15 20)) => ‘(15 20

Question 22

What is an issue with multiple lets and scopes?

Answer 22

For example, this doesn’t work, since x isn’t known
outside the body:

(let ((x 3) ;; this is variable declaration not body
(y (+ x 1))) ;; this is variable declaration not body
(+ x y)) ;; This is the body

To get around this problem, use let*:

(let* ((x 3)
(y (+ x 1)))
(+ x y))